The Envelopes of Infrared Absorption Bands

Abstract

The intensity formulae for the fine structure absorption lines of molecules of the symmetrical rotator type are approximated by replacing the sums appearing therein by integrals. The resulting expressions are evaluated explicitly and may be used either to determine the intensity of an individual line or the envelope of all the fine structure lines. The envelopes of those bands corresponding to \ensuremath{\parallel} type vibrations possess $P$, $Q$, and $R$-branches. The envelope may be characterized by two quantities, the relative intensity of the zero branch and the doublet separation which serve to fix the values of the moments of inertia $A$ and $C$. The envelopes of the \ensuremath{\parallel} type vibrations are also determined and are plotted for a series of ratios of the moments of inertia. The range of validity of the approximation is discussed and the results applied to the infrared bands of the methyl halides. The doublet separations of the \ensuremath{\parallel} type bands of these molecules are known and these (through the use of a plausible assumption regarding $C$) yield the following values of $A$, the moment of inertia \ensuremath{\parallel} to the symmetry axis. $A=32, 61, 89, 99, \ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}$ for C${\mathrm{H}}_{3}$F, C${\mathrm{H}}_{3}$Cl, C${\mathrm{H}}_{3}$Br, C${\mathrm{H}}_{3}$I. respectively. The distances between the carbon and halide nuclei are computed and compared with the corresponding distances deduced by Pauling. The agreement is satisfactory.